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Error Patterns in Computation: Using Error Patterns to Improve Instruction,9780131198869

Error Patterns in Computation: Using Error Patterns to Improve Instruction

by
Edition:
9th
ISBN13:

9780131198869

ISBN10:
0131198866
Format:
Paperback
Pub. Date:
1/1/2006
Publisher(s):
Pearson College Div
List Price: $30.80
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Summary

Reflecting many of the concerns of NCTM's Principles and Standards for School Mathematics, the ninth edition of Error Patterns in Computation is the only book available that assists teachers with identifying typical error patterns, receiving feedback on their diagnosis, and gaining insight regarding why a child may have adopted an incorrect procedure. Two major causes of error patterns - over-generalizing and over-specializing - are discussed. Simple and well organized, this book explains common errors students make in computation in every math operation and with whole numbers, rational numbers, geometry and algebra. This book is an ideal resource for teachers of mathematics in education or special education at the elementary or middle school level.

Table of Contents

PART ONE DIAGNOSIS AND INSTRUCTION
1(98)
Number and Operations: Computation
3(9)
Instruction in Mathematics
3(1)
Computational Fluency
4(3)
Algorithms
7(1)
Conceptual Learning and Procedural Learning
7(2)
Error Patterns in Computation
9(1)
Paper-and-Pencil Procedures Today
9(3)
Diagnosing Misconceptions and Error Patterns in Computation
12(33)
Learning Misconceptions and Error Patterns
15(6)
Overgeneralizing
18(2)
Overspecializing
20(1)
Encouraging Self-Assessment
21(2)
Interviewing
23(12)
Getting at a Student's Thinking
26(2)
Observing Student Behavior
28(1)
Recording Student Behavior
29(1)
Watching Language: Ours and Theirs
30(2)
Probing for Key Understandings
32(1)
Designing Questions and Tasks
33(2)
Using Graphic Organizers for Diagnosis
35(2)
Using Tests
37(4)
Guiding Diagnosis in Computation
41(1)
Reflecting on Diagnosis of Misconceptions and Error Patterns
42(3)
Providing Data-Driven Instruction in Computation
45(54)
Developing Number Sense
46(1)
Helping Students Understand Big Ideas
47(4)
Numeration
48(2)
Equals and Equivalent
50(1)
Other Concepts and Principles
51(1)
Using Models and Concrete Materials
51(2)
Helping Students Understand Operations
53(2)
Attaining Computational Fluency
55(1)
Teaching Mental Computation
56(1)
Teaching Students to Estimate
57(2)
Teaching Students to Use Calculators
59(2)
Teaching Paper-and-Pencil Procedures
61(8)
Instruction in Grades 1--2
61(2)
The Role of Manipulatives
63(1)
Developmental Instruction
63(4)
Corrective Instruction
67(1)
Students with Learning Disabilities
67(2)
Developing Mathematical Vocabulary
69(2)
Talking and Writing Mathematics
71(3)
Using Graphic Organizers for Instruction
74(5)
Understanding and Recalling Basic Number Combinations
79(5)
Using Alternative Algorithms
84(2)
Addition of Whole Numbers: Hutchings's Low-Stress Method
85(1)
Subtraction of Whole Numbers: The Equal Additions (or European-Latino) Method
85(1)
Subtraction of Rational Numbers: The Equal Additions Method
86(1)
Involving Peers
86(3)
Using Portfolios to Monitor Progress During Instruction
89(1)
Working with Parents
90(1)
Guiding Instruction
91(3)
Focus on the Student
91(1)
Involve Parents
92(1)
Teach Concepts and Skills
92(1)
Provide Instruction
92(1)
Use Concrete Materials
93(1)
Provide Practice
94(1)
Reflecting on Instruction in Computation
94(5)
PART TWO HELPING STUDENTS WHO HAVE LEARNED ERROR PATTERNS
99(128)
Whole Numbers: Addition and Subtraction
101(19)
Identifying Patterns
101(7)
Planning Instruction
108(11)
Conclusion
119(1)
Whole Numbers: Multiplication and Division
120(17)
Identifying Patterns
120(6)
Planning Instruction
126(10)
Conclusion
136(1)
Fractions and Decimals: Concepts and Equivalence
137(14)
Identifying Patterns
137(5)
Planning Instruction
142(7)
Conclusion
149(2)
Fractions and Decimals: Addition and Subtraction
151(20)
Identifying Patterns
151(8)
Planning Instruction
159(10)
Conclusion
169(2)
Fractions and Decimals: Multiplication and Division
171(15)
Identifying Patterns
172(5)
Planning Instruction
177(8)
Conclusion
185(1)
Percent and Proportion
186(8)
Identifying Patterns
186(3)
Planning Instruction
189(4)
Conclusion
193(1)
Geometry and Measurement
194(19)
Identifying Patterns
194(10)
Planning Instruction
204(8)
Conclusion
212(1)
Integers
213(7)
Identifying Patterns
213(2)
Planning Instruction
215(4)
Conclusion
219(1)
Algebra
220(7)
Identifying Patterns
220(3)
Planning Instruction
223(3)
Conclusion
226(1)
Glossary
227(5)
Selected Resources
232(40)
Assessment and Diagnosis
232(4)
Instruction
236(8)
Appendices
Appendix A Selected Student Papers and Key
244(9)
Appendix B Research on Errors in Computation
253(6)
Appendix C Game-Like Activities with Base Blocks
259(7)
Appendix D Sample Activities for Cooperative Groups
266(6)
Appendix E A Diagnostic Interview
272


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